If you don't want the master page items to come along for the ride, the only way I know of is Copy>Paste in Place. Other than that, you could delete the Master Page from the new document after the pages are moved, and assign [none] to it.
If there is already a master page with the same name in the destination file the one assigned to the page you are moving will not be transferred, and the existing one will be applied.
If I understand well: you have a doc named A with its master page A for its layout and you have another doc B with its master page B for its layout.
You want move pages from doc A to doc B and you want to have these new pages (that comes from doc A) in doc B with the master page A.
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You're totally right! Change the master pages names!
You are a rockstar Peter. Yes, your advice was spot on and worked perfectly. Thanks for saving me hours of frustration and for saving my computer from a taking a trip out of the window.
This is true for styles as well.